Introduction to twisted Alexander polynomials and related topics

This article is based on the lectures in the Winter Braids V (Pau, February 2015). We introduce some studies of twisted Alexander polynomials to non-experts through many concrete examples. In this article we follow the definition of the twisted Alexander polynomial by Wada, which can be defined for a finitely presented group with an epimorphism onto a free abelian group. The main tool is FoxÕs free calculus. In the last two sections we discuss some applications on the fiberedness of a knot and the existence of epimorphisms between knot groups.